Probably. I just put them in circular orbits, which would probably produce an unstable resonance to begin with. Watching it over a period of time showed me that the advance of the conjunction point did slow a bit, as if it were going to stop and reverse. But then it picked up speed and continued forward. I take this to mean that it is almost locked into a resonance. Starting it out with some eccentricity for Saturn will probably lock it into the resonance. Then the longitude of conjunction would librate back and forth around a point. This is interesting because that means that it's not only the longitude of Jupiter & Saturn's conjunction that causes instability to Uranus & Neptune, but the longitudes of the places that the conjunction never visits.

Thanks, Grant. That hadn't occured to me.
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Here's an animation of Jupiter and Saturn, in circular orbits at 2:1. This is not a rotating frame. It is a Kepler's pretzel centered on Jupiter. Rotating frames don't show much if the orbits are round.


Purple: Jupiter; Red: Sun; Yellow: Saturn
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This rotating frame animation isn't of Jupiter and Saturn, but of 2 hypothetical objects locked in a 2:1 resonance. But it serves to show qualitatively what is happening. If the resonance in the Jupiter & Saturn simulation did lock, the conjunction point would librate around a larger portion of the circle than this animation.

Yellow: Sun; Purple: Planet; Red: test particle with significant eccentricity